Question

Find the roots x+1/x=3;x not equal to zero

Answer 1

Hope it Helps.........

Answer 2

Answer:

The roots are $x=\frac{3+\sqrt{5}}{2},\frac{3-\sqrt{5}}{2}$

Step-by-step explanation:

Given : Expression $x+\frac{1}{x}=3;x\neq 0$

To find : The roots of the given expression?

Solution :

We write the given expression in simpler form,

$x+\frac{1}{x}=3$

$\frac{x^2+1}{x}=3$

$x^2+1=3x$

$x^2-3x+1=0$ is the quadratic equation.

Using quadratic formula,

General form - $ax^2+bx+c=0$ $D=b^2-4ac$  

Solution is $x=\frac{-b\pm\sqrt{D}}{2a}$  

Equation is $x^2-3x+1=0$

where, a=1 , b=-3, c=1

$D=b^2-4ac$

$D=(-3)^2-4(1)(1)$

$D=9-4$

$D=5$

Solution is $x=\frac{-b\pm\sqrt{D}}{2a}$

$x=\frac{-(-3)\pm\sqrt{5}}{2(1)}$  

$x=\frac{3\pm\sqrt{5}}{2}$  

Therefore, The roots are $x=\frac{3+\sqrt{5}}{2},\frac{3-\sqrt{5}}{2}$